A proxy-based method of estimating glacier heat sources and transport mechanisms to map thermal processes at a regional scale

Glacier thermal structure exerts a strong control on ice dynamics, yet it remains poorly characterized at the global scale. Despite its influence on glacier flow and, consequently, on melt and sea-level projections, thermal structure is typically neglected in large-scale glacier models. This omission stems from the fact that current methods of determining thermal structure require extensive field observations or computationally expensive modelling, resulting in only dozens of glaciers having well-defined thermal structures. In this work, we developed and applied a proxy-based approach to estimate the major heat sources (meltwater refreezing and strain heating) and transport mechanisms (advection and diffusion) in the heat transfer equation, which shapes glacier thermal structure. Proxies derived from publicly available observations and model output are calculated for glaciers in RGI-01 (Alaska) and RGI-07 (Svalbard and Jan Mayen). This framework enables a rapid regional assessment of thermal characteristics without requiring coupled thermomechanical modelling.

Across both Alaska and Svalbard, meltwater refreezing is the dominant heat source for 73% of glaciers, while diffusion dominates heat transport for 75% of glaciers. Note that this model only considers refreezing in the accumulation area, and 21% of these glaciers do not have an accumulation area. The majority (76%) of glaciers exhibit warmer accumulation-area ice transported toward cooler ablation areas. When examined by proxy rank, the most common pattern (47% of glaciers) is characterized by refreezing as the dominant heat source over strain heating, and vertical diffusion over horizontal advection as the primary transport mechanism. This pattern represents 25% of glacierized area, corresponding primarily to smaller glaciers (<10 km) scattered across Alaska, but found across sizes in Svalbard. Large Alaskan glaciers (39% of glacierized area), have a proxy pattern where refreezing dominates strong strain heating, while horizontal advection exceeds vertical diffusion. In Svalbard, this pattern is almost absent (<1% of glaciers). Comparing the proxy rank patterns of all glaciers in Alaska and Svalbard with those of glaciers with known thermal structures provides a correlation-based interpretation of the proxy results. For example, we found that the calculated proxy pattern for known temperate glaciers is characterized by dominant refreezing and advection, whereas known cold glaciers exhibit the pattern characterized by dominant refreezing over strain heating and diffusion over advection. Furthermore, a number of large glaciers on the continental side of the St. Elias Mountains in Alaska exhibit a proxy pattern distinct from those associated with well-established thermal structures in the region.

This work presents a way to calculate heat-source and transport-mechanism proxies as a practical means of estimating glacier thermal characteristics for any RGI region with sufficient input data. The resulting proxy distributions provide new insight into spatial patterns of heat generation and transfer in glaciers at the regional scale and establish a baseline for evaluating thermal responses to climate change. Moreover, these results can serve as comparative datasets for emerging emulator-based, regional-scale thermal modelling.